[Paper Review] Laser polarization of positron beam

А. П. Потылицын|ArXiv.org|Mar 19, 2002

Laser-Plasma Interactions and Diagnostics2 references3 citations

TL;DR

This paper proposes a novel method to produce polarized positron beams using multiple Compton backscattering of unpolarized ultrarelativistic positrons in an intense circularly polarized laser field. The process induces spin-dependent scattering rates, leading to a maximum achievable longitudinal polarization of $\xi_{z_{\text{max}}} = \frac{5}{8} = 0.625$ under ideal conditions, with feasibility analyzed for storage ring applications using resonant laser enhancement.

ABSTRACT

For a number of physical studies which are planned to be made with the next generation colliders, it is necessary to use polarized beams of both electrons and positrons. The problem of producing and acceleration of polarized electrons may be considered to be solved, but the existing approaches to create polarized positron beams do not ensure the parameters required. This work proposes a new approach to produce polarized positron beams, which is based on the process of multiple Compton backscattering of unpolarized ultrarelativistic positrons in the field of intense circularly polarized laser wave.

Motivation & Objective

• Address the lack of efficient methods to produce highly polarized positron beams for next-generation colliders.
• Overcome limitations of existing positron polarization techniques that fail to meet required beam parameters.
• Develop a new mechanism based on multiple Compton backscattering in intense circularly polarized laser fields to induce net positron spin polarization.
• Analyze the feasibility of achieving significant polarization in storage rings using optical resonators to reduce required laser power.
• Account for non-perturbative effects such as spin-dependent polarization shifts due to laser field interaction without photon exchange.

Proposed method

• Model the Compton backscattering process in the rest frame of the positron, using relativistic quantum electrodynamics with circularly polarized laser photons.
• Derive spin-dependent differential cross-sections for Compton scattering, including terms for circular polarization $P_c$ and initial/final positron spin projections $\xi_{0z}, \xi_z$.
• Use the cross-section expressions to compute the spin-flip ($w_{\uparrow\downarrow}$) and non-flip ($w_{\downarrow\uparrow}$) transition probabilities.
• Calculate the maximum achievable polarization via $\xi_{z_{\text{max}}} = \frac{w_{\uparrow\downarrow} - w_{\downarrow\uparrow}}{w_{\uparrow\downarrow} + w_{\downarrow\uparrow}}$, yielding $\xi_{z_{\text{max}}} = \frac{5}{8}$ for the linear regime.
• Model beam evolution through a laser pulse using a rate equation: $\xi_z = \xi_{z_{\text{max}}}[1 - \exp(-N/N_{\text{pol}})]$, where $N_{\text{pol}}$ is the polarization relaxation length.
• Assess feasibility in storage rings by coupling the laser beam to a high-Q optical resonator, reducing required laser power and enabling repeated passes.

Experimental results

Research questions

• RQ1 Can multiple Compton backscattering in an intense circularly polarized laser field induce net polarization in an initially unpolarized positron beam?
• RQ2 What is the maximum achievable longitudinal polarization of positrons under this mechanism, and what physical parameters determine it?
• RQ3 How do non-perturbative laser field effects (e.g., field-induced spin shifts without photon exchange) affect the attainable polarization?
• RQ4 Is it feasible to achieve significant polarization in a storage ring using a resonant optical cavity to enhance laser intensity?
• RQ5 Can nonlinear multiple photon absorption processes in the laser field lead to higher polarization than the linear regime predicts?

Key findings

• The maximum theoretical polarization of the positron beam via linear multiple Compton backscattering is $\xi_{z_{\text{max}}} = \frac{5}{8} = 0.625$, derived from unequal spin-flip and non-flip transition probabilities.
• The polarization builds up exponentially with the number of collisions, following $\xi_z = \xi_{z_{\text{max}}}[1 - \exp(-N/N_{\text{pol}})]$, with $N_{\text{pol}} = 6.1 \times 10^5$ for a 1.98 GeV positron beam.
• For a 1 J laser pulse with $z_R = 1$ mm, each positron undergoes an average of $N = 0.82$ collisions per pass, requiring $n \approx 7.4 \times 10^5$ turns to reach full polarization.
• The required time for polarization in a 297 m storage ring is $\tau_{\text{pol}} \approx 15.5$ ms, demanding stable laser injection over $\sim 10^3$ pulses for a Q-factor of $10^3$.
• Nonlinear processes (multi-photon absorption) would reduce $N_{\text{pol}}$ and thus polarization efficiency, but may allow higher polarization than the linear limit if properly controlled.
• The analogy with helical undulators suggests that nonlinear multiple Compton scattering could, in principle, achieve polarization up to 92%, matching synchrotron radiation-based self-polarization mechanisms.